When `10^(14)` electrons are removed from a neutral metal sphere , the charge on it becomes

Options

A. (a) `16 muC`
B. (b) `-16 muC`
C. (c) `32 muC`
D. (d) `-32 muC`

Answer

To solve the problem of determining the charge on a neutral metal sphere after removing \(10^{14}\) electrons, we can follow these steps:

### Step 1: Understand the Charge of an Electron
Electrons carry a negative charge. The charge of one electron is approximately:
\[ e = 1.6 \times 10^{-19} \text{ coulombs} \]

### Step 2: Calculate the Total Charge Removed
When \(10^{14}\) electrons are removed, the total charge removed can be calculated using the formula:
\[ Q = n \cdot e \]
where \(n\) is the number of electrons removed. Substituting the values:
\[ Q = 10^{14} \cdot (1.6 \times 10^{-19}) \text{ coulombs} \]

### Step 3: Perform the Calculation
Now, we can perform the multiplication:
\[ Q = 10^{14} \cdot 1.6 \times 10^{-19} = 1.6 \times 10^{-5} \text{ coulombs} \]

### Step 4: Determine the Sign of the Charge
Since we are removing electrons (which are negatively charged), the sphere will become positively charged. Therefore, the charge on the sphere will be:
\[ Q = +1.6 \times 10^{-5} \text{ coulombs} \]

### Step 5: Convert to Microcoulombs
To express the charge in microcoulombs (where \(1 \text{ microcoulomb} = 10^{-6} \text{ coulombs}\)):
\[ Q = 1.6 \times 10^{-5} \text{ coulombs} = 16 \times 10^{-6} \text{ coulombs} = 16 \text{ microcoulombs} \]

### Final Answer
Thus, the charge on the metal sphere after removing \(10^{14}\) electrons is:
\[ \text{Charge} = +16 \text{ microcoulombs} \]

---